Is it possible to engrave on iPad after purchase?

No, not through Apple at least.

Apple engravings must be set up during purchase for items that support engraving.

After purchase Apple offers no engraving service.

3rd party engraving services may void your warranty.

This is what Apple says about engravings:

Make it your own — or a gift they’ll never forget — with free laser engraving. You can add a message to any new iPad, AirPods, AirTag, or Apple Pencil (2nd generation). This option is available online and through the Apple Store App. NOTE: This service is only available online and is not offered on refurbished products.

Online Exclusives - Shopping Help - Apple

There is no option to purchase a device in store and have it engraved after purchase. Also in all the years participating here, I have never seen a user who was able to get an engraving of a device after purchase. I certainly would not want to stop you from contacting Apple directly as none of us work for Apple and have no possible way to make that determinations, but did want to manage your expectations.

In any case, you likely have the option to return the device in the 14 day window and purchase another one online with the engraving you want. It does seem like an unnecessary step to have to take, but is a possibility to get exactly what you want.

You would have to ask Apple if that is possible.

This support article has various country telephone numbers for contacting Apple for support and service ➔ Contact Apple Support - Apple Support Scroll down to “Connect with live support”. If your country is not in the list, go to the “Other countries” entry at the end of the list. Not every country has telephone support, and phone numbers may only work when calling from the same country.

For chat, you can try using the Apple Support App —> https://apps.apple.com/app/apple-support/id1130498044